This is a Phase II, multicenter, open label, dose escalation clinical trial examining multiple infusions of four doses of ABX-CBL in patients with steroid-resistant acute Graft Versus Host Disease (GVHD). Children and adults receiving a stem cell transplant within 100 days, with steroid resistant acute GVHD with a severity index of B, C, or D on the modified IBMTR Severity Scale may be eligible to participate in this study. A total of 48 patients, 12 per treatment cohort, will be enrolled in this study at six to ten clinical sites within the United States. Up to ten patients may be invited to participate at the University of Wisconsin. Patients will be infused with ABX-CBL daily for seven days (induction regimen) followed by a maintenance regimen of infusions two times per week for two weeks. Patients in all cohorts will receive up to eleven intravenous infusions of ABX-CBL. The study medication will be infused over two hours via a syringe pump. Safety evaluations will occur prior to advancing to the next cohort. The four cohorts are as follows: Cohort 1: 0.01 mg/kg; Cohort 2: 0.1 mg/kg; Cohort 3: 0.3 mg/kg; Cohort 4: 1.0 mg/kg. Patients will be followed for eight weeks (visits are weekly for four weeks followed by a visit four weeks later) for safety and clinical effect. Safety will be assessed by monitoring adverse events while on study as well as vital signs during the infusion of ABX-CBL, by frequent physical exams, laboratory studies including complete blood counts, T-cell subsets, serum chemistries, and urinalyses at regular intervals. Baseline CPK with isoenzymes will be obtained on all patients and patients who experience any infusion related adverse experiences will have repeat CPK with isoenzymes obtained. In addition, patients will be monitored for Human Anti Mouse Antibody (HAMA) response by ELISA. Clinical effect of ABX-CBL will be assessed by evaluating changes to the overall score of acute GVHD based upon a modified IBMTR Severity Index, time to response, duration of response, time and incidence of flare of acute GVHD, and length of hospitalization. Five patients in each cohort will be assigned to have pharmacokinetic blood samples for pK profile. The assignment to pK will be a combination of the first five patients in each cohort and the attempt to evenly distribute between males and females and adults and pediatrics. Patients who have received at least one infusion of ABX-CBL will be scheduled to participate in a long-term follow-up program to evaluate the long term safety of ABX-CBL and long term survival.